Communications in Mathematical Sciences

Volume 6 (2008)

Number 4

On/off-state design of semiconductor doping models

Pages: 1021 – 1041



M. Burger

R. Pinnau

M.-T. Wolfram


We consider the multi-objective optimal dopant profiling of semiconductor devices. The two objectives are to gain a higher on-state current while the off-state current is kept small. This design question is treated as a constrained optimization problem, where the constraints are given by the stationary drift-diffusion model for the on-state and the linearized drift-diffusion model for the off-state. Using the doping profile as a state variable and the electrostatic potential as the new design variable, we obtain a simpler optimization problem, whose Karush-Kuhn-Tucker conditions partially decouple. Based on this observation we can construct a very efficient iterative optimization algorithm, which avoids solving the fully coupled drift-diffusion system. Due to the simple structure of the adjoint equations, this algorithm can be easily included into existing semiconductor simulation tools. The efficiency and success of this multi-objective design approach is underlined by various numerical examples.


Semiconductor design; drift-diffusion model; Gummel iteration; optimal control; multi-objective; dopant profiling

2010 Mathematics Subject Classification

35J50, 49J20, 49K20

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